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Florida Grade 6 Math · Algebraic Reasoning

MA.6.AR.3.1: Ratios

What this Grade 6 benchmark means, worked examples, common mistakes, and a free printable worksheet.

Created by a Florida mom · Published by Tropical Learning LLC

Download Free Worksheet (PDF)See worked examples

What Is Benchmark MA.6.AR.3.1?

A ratio compares two quantities. It can be written as a/b, a to b, or a:b. The quantities can be in the same units or different units, and in Grade 6 they are whole numbers.

Part-to-part ratios compare two parts (cats to dogs). Part-to-whole ratios compare one part to the total (cats to all pets). The order of the words tells the order of the numbers.

Official benchmarkGiven a real-world context, write and interpret ratios to show the relative sizes of two quantities using appropriate notation: a/b, a to b, or a:b where b ≠ 0.

On the FAST test: part of the Grade 6 reporting category Algebraic Reasoning, which is about 25–36% of the test.

Worked Examples

Worked Example 1

Part-to-Part and Part-to-Whole

A shelter has 12 cats and 8 dogs. Write the ratio of cats to dogs and the ratio of dogs to all pets.
  1. 1Cats to dogs: 12 to 8, or 12:8 (equivalent to 3:2)
  2. 2All pets: 12 + 8 = 20
  3. 3Dogs to all pets: 8:20 (equivalent to 2:5)
Answer: 12:8 and 8:20

Worked Example 2

Interpreting a Ratio

The ratio of sunny days to rainy days last month was 3:2. What does that mean?
  1. 1For every 3 sunny days, there were 2 rainy days.
  2. 2Out of every 5 days, 3 were sunny.
Answer: 3 sunny days for every 2 rainy days

Common Mistakes to Watch For

Writing the numbers in the wrong order

Wrong:Cats to dogs with 12 cats and 8 dogs: 8:12

The first quantity named comes first: cats to dogs is 12:8.

Mixing up part-to-part and part-to-whole

Wrong:With 12 cats and 8 dogs, the fraction of pets that are dogs is 812.

Compare dogs to all 20 pets: 820.

Helpful Math Tip

Use real counts at home, like forks to spoons in a drawer, and say the ratio both ways to see why order matters.

Related Grade 6 Skills

MA.6.AR.3.2

Rates and Unit Rates

MA.6.AR.3.3

Tables of Equivalent Ratios

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Independent Educational Platform. FastChomp is published by Tropical Learning LLC and is not affiliated with, sponsored by, or endorsed by the Florida Department of Education. FAST and Star assessment names are referenced for informational purposes only. FastChomp practice questions are original educational materials, not official Florida FAST assessment questions.